Q3) A boat takes 9 hours to travel 30 km upstream and 40 km downstream but it takes 12 hours to travel 42 km upstream and 50 km downstream. Find the speed of the boat in still water and the speed of the stream
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SOLUTION ::
Let the speed of the boat in still water = x km/h
The speed of the stream = y km/h
We know that
Total time = Upstream distance/upstream speed + Downstream dist/downstream speed
Upstream speed
= speed of boat - speed of stream
= x - y
Down stream speed = x + y
BY THE GIVEN CONDITION
30/x-y + 40/x+y = 9 ............. (i)
42/x-y + 50/x+y = 12 .............(ii)
Multiplying eq.(i) by 5 & eq.(ii) by 4
150/x-y + 200/x+y = 45 ......(iii)
168/x-y + 200/x+y = 48 ......(iv)
Now (iii) - (iv) gives
-18/x-y = - 3
x-y = 6 .....(v)
Substituting (v) in (iii)
150/x-y + 200/x+y = 45
150/6 + 200/x+y = 45
200/x+y = 20
x + y = 10........(vi)
Adding (v) & (vi) We get
2x = 16
x = 8
8+y = 10
y= 2
Hence speed of boat = 8 km/h
Speed of stream = 2 km/h
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